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| | Doing four-vector algebra: | | Doing four-vector algebra: |
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| − | <math> p^{\mu}_{\gamma} + p^{\mu}_D = p^{\mu}_p + p^{\mu}_n \Rightarrow </math> | + | <math> p^{\mu}_{\gamma} + p^{\mu}_D = p^{\mu}_p + p^{\mu}_n \Rightarrow </math><br> |
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| | <math> p^{\mu\ 2}_p = \left(p^{\mu}_{\gamma} + p^{\mu}_D - p^{\mu}_n\right)^2 = | | <math> p^{\mu\ 2}_p = \left(p^{\mu}_{\gamma} + p^{\mu}_D - p^{\mu}_n\right)^2 = |
| − | | + | p^{\mu\ 2}_{\gamma} + p^{\mu\ 2}_D + p^{\mu\ 2}_n + 2p^{\mu}_{\gamma}p^{\mu}_D - 2p^{\mu}_n(p^{\mu}_{\gamma} + p^{\mu}_D) </math> |
| − | (p^{\mu}_{\gamma})^2 + (p^{\mu}_D)^2 + (p^{\mu}_n)^2 + 2p^{\mu}_{\gamma}p^{\mu}_D - 2p^{\mu}_n(p^{\mu}_{\gamma} + p^{\mu}_D) </math> | |
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Revision as of 21:30, 5 June 2010
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Relativistic kinematic
energy dependence of outcoming neutron versus energy of incoming photons
[math] E = T + m[/math]
[math] E = p^2 + m^2[/math]
writing four-vectors:
[math] p_{\gamma} = \left( T_{\gamma},\ T_{\gamma},\ 0,\ 0 \right) [/math]
[math] p_D = \left( m_D,\ 0,\ 0,\ 0 \right) [/math]
[math] p_{n} = \left( E_n,\ p_n\cos(\Theta_n),\ p_n\sin(\Theta_n),\ 0 \right) [/math]
[math] p_{p} = \left( E_p,\ p_p\cos(\Theta_p),\ p_p\sin(\Theta_p),\ 0 \right) [/math]
Doing four-vector algebra:
[math] p^{\mu}_{\gamma} + p^{\mu}_D = p^{\mu}_p + p^{\mu}_n \Rightarrow [/math]
[math] p^{\mu\ 2}_p = \left(p^{\mu}_{\gamma} + p^{\mu}_D - p^{\mu}_n\right)^2 =
p^{\mu\ 2}_{\gamma} + p^{\mu\ 2}_D + p^{\mu\ 2}_n + 2p^{\mu}_{\gamma}p^{\mu}_D - 2p^{\mu}_n(p^{\mu}_{\gamma} + p^{\mu}_D) [/math]
[math] m_p^2 = m_y^2(=0) + m_D^2 + m_n^2 [/math]
</math>
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